Non-self-adjoint problems with a parameter that are elliptic in the sense of Agmon-Douglis-Nirenberg (Q2639237)

The paper considers the problem \((A-\lambda E)U(x)=0\) in the bounded domain \(G\subset {\mathbb{R}}^ n\) with (n-1) dimensional \(C^{\infty}\) boundary, with boundary condition \(BU(x)=0\) on \(\Gamma =\partial G\). \(A=A(x,D)\), \(B=B(x,D)\), \(p\times p\), respectively \(q\times p\) matrices, satisfying some restrictive conditions. Suppose that the problem is Agmon-Douglis-Nirenberg elliptic along a ray L. The paper studies the completeness of some functions in relation with the above problem.